Divergent reflections around the photon sphere of a black hole

Abstract From any location outside the event horizon of a black hole there are an infinite number trajectories for light to observer. Each these paths differ in orbits revolved around and their proximity last photon orbit. With simple numerical perturbed analytical solution null-geodesic equation Schwarzschild we will reaffirm how each additional orbit is factor $$e^{2 \pi }$$ e 2 π closer hole’s optical edge. Consequently, surface background be mirrored infinitely exponentially thinner slices Furthermore, introduced formalism proves entire strong field limit prescribed by diverging converging exponential. Lastly, existence exponential family generalized equatorial plane Kerr with exponentials dependence on spin derived. Thereby, proving that distance between subsequent images increases decreases respectively retrograde prograde images. In extremely rotating no logarithmic divergence exists trajectories.